dB-linear voltage-to-current converter

ABSTRACT

A dB-linear voltage-to-current (V/I) converter that is amenable to implementation in CMOS technology. In a representative embodiment, the dB-linear V/I converter has a voltage scaler, a current multiplier, and an exponential current converter serially connected to one another. The voltage scaler supplies an input current to the current multiplier based on an input voltage. The current multiplier multiplies the input current and a current proportional to absolute temperature and supplies the resulting current to the exponential current converter. The exponential current converter has a differential MOSFET pair operating in a sub-threshold mode and generating an output current that is proportional to a temperature-independent, exponential function of the input voltage.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to electronics and, more specifically, tovoltage-to-current (V/I) converters having an exponential transferfunction.

2. Description of the Related Art

This section introduces aspects that may help facilitate a betterunderstanding of the invention(s). Accordingly, the statements of thissection are to be read in this light and are not to be understood asadmissions about what is in the prior art or what is not in the priorart.

An exponential (or dB-linear) voltage-to-current (V/I) converter is akey component for the design of automatic gain-control (AGC) circuits,which are used in a variety of applications, such as wirelesscommunications devices, hearing aids, and disk drives. A representativeAGC circuit employs an exponential V/I converter in the feedback loopthat controls the gain of a variable-gain amplifier (VGA). Theexponential characteristic of the V/I converter enables the AGC circuitto advantageously have a substantially constant settling time for avariety of initial input-signal conditions, which is very desirable forthe above-specified applications. Additional details on the use ofexponential V/I converters in AGC circuits can be found, e.g., in U.S.Pat. No. 6,369,618, which is incorporated herein by reference in itsentirety.

One problem with exponential V/I converters is that they are notstraightforwardly amenable to implementation in CMOS technology. Morespecifically, unlike bipolar transistors, which have an inherentexponential transfer characteristic, MOSFET transistors have asquare-law transfer characteristic in strong inversion. As a result,designing a CMOS V/I converter that exhibits an exponential transfercharacteristic and has other desirable properties is relativelydifficult.

SUMMARY OF THE INVENTION

Problems in the prior art are addressed by various embodiments of anexponential (or dB-linear) voltage-to-current (V/I) converter that isamenable to implementation in CMOS technology. In a representativeembodiment, the exponential V/I converter has a voltage scaler, acurrent multiplier, and an exponential current converter seriallyconnected to one another. The voltage scaler supplies an input currentto the current multiplier based on an input voltage. The currentmultiplier multiplies the input current and a current proportional toabsolute temperature and supplies the resulting current to theexponential current converter. The exponential current converter has adifferential MOSFET pair operating in a sub-threshold mode andgenerating an output current that is proportional to atemperature-independent, exponential function of the input voltage.Advantageously, the exponential V/I converter can be implemented to havea dB-linear operation range as wide as about 40 dB.

According to one embodiment, provided is a device having (A) a currentmultiplier that multiplies a first current and a current proportional toabsolute temperature to generate a second current; and (B) anexponential converter that applies an exponential transfer function tothe second current to generate an output current. The exponentialtransfer function depends on a thermal voltage. Temperature dependenceof the current proportional to absolute temperature counteractstemperature dependence of the thermal voltage to cause the outputcurrent to be proportional to a temperature-independent, exponentialfunction of the first current over an operating range of the device.

According to another embodiment, provided is a method having the stepsof: (A) multiplying a first current and a current proportional toabsolute temperature to generate a second current; and (B) applying anexponential transfer function to the second current to generate anoutput current. The exponential transfer function depends on a thermalvoltage. Temperature dependence of the current proportional to absolutetemperature counteracts temperature dependence of the thermal voltage tocause the output current to be proportional to atemperature-independent, exponential function of the first current overa specified operating range.

According to yet another embodiment, provided is a device having (A)means for multiplying a first current and a current proportional toabsolute temperature to generate a second current; and (B) means forapplying an exponential transfer function to the second current togenerate an output current. The exponential transfer function depends ona thermal voltage. Temperature dependence of the current proportional toabsolute temperature counteracts temperature dependence of the thermalvoltage to cause the output current to be proportional to atemperature-independent, exponential function of the first current overan operating range of the device.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and benefits of the present invention willbecome more fully apparent from the following detailed description, theappended claims, and the accompanying drawings in which:

FIG. 1 shows a block diagram of an exponential (or dB-linear)voltage-to-current (V/I) converter according to one embodiment of theinvention;

FIG. 2 shows a circuit diagram of a voltage scaler that can be used inthe exponential V/I converter of FIG. 1 according to one embodiment ofthe invention;

FIG. 3 shows a circuit diagram of a current multiplier that can be usedin the exponential V/I converter of FIG. 1 according to one embodimentof the invention;

FIG. 4 shows a circuit diagram of an exponential current converter thatcan be used in the exponential V/I converter of FIG. 1 according to oneembodiment of the invention; and

FIG. 5 shows a circuit diagram of a current limiter that can be used inthe exponential V/I converter of FIG. 1 according to one embodiment ofthe invention.

DETAILED DESCRIPTION

FIG. 1 shows a block diagram of an exponential (or dB-linear)voltage-to-current (V/I) converter 100 according to one embodiment ofthe invention. Converter 100 receives input voltage V_(in) and convertsit into output current I_(out) so that there is an exponentialrelationship between the input voltage and the output current. Asfurther described below, converter 100 is amenable to implementation inCMOS technology and is advantageously capable of maintaining theexponential transfer characteristic over a relatively wide (e.g., about40 dB) output-current range.

Converter 100 has a voltage scaler 110 that conditions input voltageV_(in) for further processing in the subsequent circuit blocks of theconverter. More specifically, voltage scaler 110 scales input voltageV_(in) and adds bias voltage V_(bias) to the scaled voltage according toEq. (1):V ₁₁₀ =V _(bias) +γV _(in)   (1)where V₁₁₀ is the output voltage of the voltage scaler, and γ is ascaling factor. In one embodiment, one or both of bias voltage V_(bias)and scaling factor γ are programmable so that output voltage V₁₁₀remains in an optimal range for the entire variability range of inputvoltage V_(in). In a representative embodiment, |V_(bias)|≈0.2V andγ≈0.5.

Converter 100 applies output voltage V₁₁₀ to resistive load R₀, whichdrives current I₁ through that load. In effect, the combination ofvoltage scaler 110 and resistive load R₀ serves as a voltage-to-currentconverter that converts input voltage V_(in) into current I₁. Thesubsequent signal processing in converter 100 is current-based andconverts current I₁ into output current I_(out).

Converter 100 further has a current multiplier 120 whose output currentI₂ is expressed according to Eq. (2):I₂=ηI₁I_(PTAT)   (2)where η is a constant, and I_(PTAT) is a current proportional toabsolute temperature (PTAT). In effect, current multiplier 120 generatesoutput current I₂ by multiplying the input current (i.e., current I₁)and current I_(PTAT) As further described below, the temperatureproportionality of current I_(PTAT) is utilized to make the exponentialtransfer characteristic of converter 100 substantially temperatureindependent and enable the converter to operate accurately and reliablyin a variety of ambient conditions without a thermostat.

Output current I₂ produced by current multiplier 120 is applied to anexponential current converter 130 that converts output current I₂ intooutput current I₃ according to Eq. (3):

$\begin{matrix}{I_{3} = {A\;{\exp\left( {\sigma\frac{I_{2}}{V_{T}}} \right)}}} & (3)\end{matrix}$where A and σ are constants, and V_(T) is the thermal voltage(=k_(B)T/q, where k_(B) is the Boltzmann constant, T is temperature inKelvin, and q is the electron charge). Eqs. (2) and (3), taken together,indicate that current multiplier 120 and exponential current converter130 work together to provide a substantially temperature-independent,exponential transfer function between currents I₁ and I₃. Morespecifically, according to Eqs. (2) and (3), the argument of theexponent in Eq. (3) contains current I_(PTAT) and thermal voltage V_(T)in the nominator and denominator, respectively. Since both currentI_(PTAT) and thermal voltage V_(T) are linear functions of temperature,their temperature dependencies cancel each other, thereby causing theexponential transfer function between currents I₁ and I₃ to besubstantially temperature independent.

Exponential current converter 130 applies output current I₃ to a currentlimiter 140, where it is processed to generate output current I_(out).More specifically, current limiter 140 imposes lower limit I_(min) andupper limit I_(max) onto current I₃. If the magnitude of current I₃ issmaller than lower limit I_(min), then current limiter 140 forcesI_(out)≧I_(min). If the magnitude of current I₃ is larger than upperlimit I_(max), then current limiter 140 forces I_(out)≈I_(max). If themagnitude of current I₃ is between lower limit I_(min) and upper limitI_(max), then current limiter 140 forces I_(out)≈I₃.

FIG. 2 shows a circuit diagram of a voltage scaler 200 that can be usedas voltage scaler 110 according to one embodiment of the invention.Voltage scaler 200 has a reference current source 202, an operationalamplifier 204, and four resistors R₁-R₄ interconnected as shown in FIG.2. If R₁>>R₂, then voltage scaler 200 implements the transfer functiondefined by Eq. (1), wherein:

$\begin{matrix}{V_{bias} \approx {I_{ref}\frac{R_{2}\left( {R_{3} + R_{4}} \right)}{R_{3}}}} & \left( {4a} \right) \\{\gamma \approx \frac{R_{2}\left( {R_{3} + R_{4}} \right)}{R_{1}R_{3}}} & \left( {4b} \right)\end{matrix}$where I_(ref) is the current generated by reference current source 202.Note that resistor R₁ is a programmably variable resistor, which enablesprogrammability of scaling factor γ. In one embodiment, referencecurrent source 202 is a programmably variable current source, whichenables programmability of bias voltage V_(bias).

FIG. 3 shows a circuit diagram of a current multiplier 300 that can beused as current multiplier 120 according to one embodiment of theinvention. Current multiplier 300 has two nested differentialamplifiers, each having an active current-mirror load. The activedevices of the first (outer) differential amplifier are MOSFETtransistors M5 and M6, and the load of that differential amplifier isthe current mirror formed by transistors MOSFET M1 and M2. Similarly,the active devices of the second (inner) differential amplifier aretransistors MOSFET M7 and M8, and the load of that differentialamplifier is the current mirror formed by MOSFET transistors M3 and M4.The gates of transistors M5 and M7 are both electrically connected to acommon node having floating voltage V_(x). The gates of transistors M6and M8 are both electrically connected to a common node that receivesreference voltage V_(ref).

In one embodiment, reference voltage V_(ref) is supplied by aprogrammable reference-voltage source (not explicitly shown in FIG. 3).The voltage source is programmed to set a value of V_(ref) so that thereis a desired relationship between output current I₂ and input voltageV_(in). In particular, V_(ref) is selected from a voltage range,wherein, if V_(ref) changes, then the transfer function between outputcurrent I₂ and input voltage V_(in) is translated along the voltage axiswithout changing its slope.

Current multiplier 300 further has reference current sources 302 and 304that function as tail supplies of the outer and inner differentialamplifiers, respectively. Current source 302 is designed to generatereference current I_(bgap) that does not depend on the technologicalprocess used in the fabrication of current multiplier 300 or on thetemperature of the current multiplier. In one embodiment, current source302 can be implemented, as known in the art, using a conventionalbandgap circuit. Current source 304 is designed to generatetemperature-dependent PTAT current I_(PTAT) (see also Eq. (2)). In oneembodiment, current source 304 can be a PTAT current source disclosed,e.g., in U.S. Patent Application Publication No. 2008/0284493, which isincorporated herein by reference in its entirety. In one configuration,current source 304 generates current I_(PTAT) so that, at roomtemperature (T₀=298 K), I_(PTAT)=I_(bgap).

Operation of transistors M5-M8 in current multiplier 300 is described byEqs. (5a)-(5d), respectively:

$\begin{matrix}{\frac{I_{bgap} + I_{1}}{2} = {\frac{1}{2}\mu_{n}C_{ox}\frac{W_{1}}{l_{1}}\left( {V_{x} - V_{a} - V_{th}} \right)^{2}}} & \left( {5a} \right) \\{\frac{I_{PTAT} + I_{2}}{2} = {\frac{1}{2}\mu_{n}C_{ox}\frac{W_{2}}{l_{2}}\left( {V_{x} - V_{b} - V_{th}} \right)^{2}}} & \left( {5b} \right) \\{\frac{I_{bgap} - I_{1}}{2} = {\frac{1}{2}\mu_{n}C_{ox}\frac{W_{1}}{l_{1}}\left( {V_{ref} - V_{a} - V_{th}} \right)^{2}}} & \left( {5c} \right) \\{\frac{I_{PTAT} - I_{2}}{2} = {\frac{1}{2}\mu_{n}C_{ox}\frac{W_{2}}{l_{2}}\left( {V_{ref} - V_{b} - V_{th}} \right)^{2}}} & \left( {5d} \right)\end{matrix}$where μ_(n) is the mobility of electrons; C_(ox) is the capacitance ofthe oxide layer; W₁ and l₁ are the width and length, respectively, oftransistors M5 and M6; W₂ and l₂ are the width and length, respectively,of transistors M7 and M8; V_(a) and V_(b) are the voltages indicated inFIG. 3; and V_(th) is the threshold voltage. If transistors M5-M8 areimplemented so that

${\frac{\left( {W_{1}/l_{1}} \right)}{\left( {W_{2}/l_{2}} \right)} = 1},$then V_(x)≈V_(ref) and Eqs. (5a)-(5d) reduce to Eq. (2), whereinη=(I_(bgap))⁻¹.

If current multiplier 300 is used in V/I converter 100 to implementcurrent multiplier 120, then the following relationship exists betweeninput voltage V_(in) and current I₁:I ₁ =αV _(in) +i _(c)   (6)where α=γ/R₀ and i_(c)=(V_(bias)−V_(ref))/R₀. Note that, for a givenconfiguration of V/I converter 100, α and i_(c) are constants.

FIG. 4 shows a circuit diagram of an exponential current converter 400that can be used as exponential current converter 130 according to oneembodiment of the invention. Exponential current converter 400 has adifferential pair of MOSFET transistors M1 and M2 that are configured tooperate in a sub-threshold mode (also referred to as a cut-off orweak-inversion mode). The gates of transistors M1 and M2 areelectrically connected through resistor R₁₂. The gate of transistor M2receives bias voltage V_(bias1) from a bias-voltage generator 410.Transistor M3 serves as a tail supply for the differential pair. Acurrent source 402 drives reference current I_(ref1) through transistorM2. A current source 404 and transistor M4 are used to appropriatelybias transistors M2 and M3.

As known in the art, drain-to-source current I_(ds) in a MOSFETtransistor operating in a sub-threshold mode varies exponentially withgate-to-source voltage V_(gs), as expressed by Eq. (7):

$\begin{matrix}{I_{ds} \approx {I_{0}{\exp\left( \frac{V_{gs} - V_{th}}{{nV}_{T}} \right)}}} & (7)\end{matrix}$where I₀ is a constant; and n=1+C_(D)/C_(ox), where C_(D) is thecapacitance of the depletion layer. Applying Eq. (7) to transistor M2,one finds that:

$\begin{matrix}{I_{{ref}\; 1} \approx {I_{0}{\exp\left( \frac{V_{{bias}\; 1} - V_{s} - V_{th}}{{nV}_{T}} \right)}}} & (8)\end{matrix}$where V_(s) is the voltage indicated in FIG. 4. Further applying Eq. (7)to transistor M1 and then using Eq. (8), one finds that:

$\begin{matrix}{{I_{3} \approx {I_{0}{\exp\left( \frac{V_{{bias}\; 1} + {I_{2}R_{12}} - V_{s} - V_{th}}{{nV}_{T}} \right)}}} = {I_{{ref}\; 1}{\exp\left( \frac{I_{2}R_{12}}{{nV}_{T}} \right)}}} & (9)\end{matrix}$Note that Eq. (9) is equivalent to Eq. (3), wherein A=I_(ref1) andσ=R₁₂/n.

If current multiplier 300 and exponential current converter 400 are usedin V/I converter 100 to implement current multiplier 120 and exponentialconverter 130, respectively, then the following relationship existsbetween input voltage V_(in) and current I₃:

$\begin{matrix}{{I_{3} = {B\;{\exp\left( {\beta\; V_{i\; n}} \right)}}}{where}{B = {{I_{{ref}\; 1}{\exp\left( \frac{R_{12}I_{PTAT}i_{c}}{{nV}_{T}I_{bgap}} \right)}\mspace{14mu}{and}\mspace{14mu}\beta} = {\frac{\alpha\; R_{12}I_{PTAT}}{{nV}_{T}I_{bgap}}.}}}} & (10)\end{matrix}$Note that, for a given configuration of V/I converter 100, B and β areconstants that do not depend on the temperature because the temperaturedependencies of current I_(PTAT) and thermal voltage V_(T) substantiallycancel each other. Thus, Eq. (10) indicates that V/I converter 100employing current multiplier 300 and exponential current converter 400provides a temperature-independent, exponential transfer functionbetween input voltage V_(in) and current I₃. In addition, currentmultiplier 300 and exponential current converter 400 are advantageouslycapable of exhibiting a dB-linear transfer function over a relativelywide (e.g., about 40 dB) operation range because the exponential currentconverter invokes the inherent exponential characteristic of MOSFETtransistors in the sub-threshold operating mode.

FIG. 5 shows a circuit diagram of a current limiter 500 that can be usedas current limiter 140 according to one embodiment of the invention.Current limiter 500 has reference current sources 502 and 504, anoperational amplifier 506 with a feedback network, and two currentmirrors formed by transistors M1, M4, M5, and M6. Reference currentI_(ref3) generated by current source 502 sets the minimum output currentfor current limiter 500. Reference current I_(ref2) generated by currentsource 504 sets the maximum output current for current limiter 500.

Current source 502 sets the minimum output current for current limiter500 because it is directly connected to an output terminal 508 of thecurrent limiter. As a result, output current I_(out) has at least acurrent component corresponding to reference current I_(ref3). Hence,output current I_(out) does not drop below the value of I_(ref3) even ifcurrent I₃ becomes zero.

Current source 504 sets the maximum output current for current limiter500 in the following manner. Transistors M1 and M2 have substantiallythe same size, which causes the value of I_(ref2) to set the ON/OFFlevel for transistor M3. More specifically, if current I₃ is smallerthan I_(ref2), then operational amplifier 506 holds transistor M3 in theOFF state. As a result, the two current mirrors formed by transistorsM1, M4, M5, and M6 force output current I_(out) to mirror current I₃.However, if current I₃ is greater than I_(ref2), then operationalamplifier 506 turns ON transistor M3, which sinks the excess current andcauses the current flowing through transistor M1 to remain at the valueof I_(ref2). The two current mirrors then mirror the current flowingthrough transistor M1 onto output terminal 508, thereby substantiallyforcing output current I_(out) not to exceed the value of I_(ref3).

While this invention has been described with reference to illustrativeembodiments, this description is not intended to be construed in alimiting sense. Although certain embodiments of the invention have beendescribed in reference to NMOS technology, the invention is not solimited. Various circuits of the inventions can also be implementedusing the PMOS technology, the bipolar CMOS technology, and variousnon-MOS technologies, including implementations in an integratedcircuit. Various modifications of the described embodiments, as well asother embodiments of the invention, which are apparent to personsskilled in the art to which the invention pertains are deemed to liewithin the principle and scope of the invention as expressed in thefollowing claims.

As used herein, the term dB-linear means that, when plotted on alogarithmic scale over an operation range, the output current is asubstantially linear function of the input voltage (or current), whereinslope of the linear function does not deviate from a specified value bymore than about ±5%.

Unless explicitly stated otherwise, each numerical value and rangeshould be interpreted as being approximate as if the word “about” or“approximately” preceded the value of the value or range.

It will be further understood that various changes in the details,materials, and arrangements of the parts which have been described andillustrated in order to explain the nature of this invention may be madeby those skilled in the art without departing from the scope of theinvention as expressed in the following claims.

Although the elements in the following method claims, if any, arerecited in a particular sequence with corresponding labeling, unless theclaim recitations otherwise imply a particular sequence for implementingsome or all of those elements, those elements are not necessarilyintended to be limited to being implemented in that particular sequence.

Reference herein to “one embodiment” or “an embodiment” means that aparticular feature, structure, or characteristic described in connectionwith the embodiment can be included in at least one embodiment of theinvention. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment, nor are separate or alternative embodiments necessarilymutually exclusive of other embodiments. The same applies to the term“implementation.”

Also for purposes of this description, the terms “couple,” “coupling,”“coupled,” “connect,” “connecting,” or “connected” refer to any mannerknown in the art or later developed in which energy is allowed to betransferred between two or more elements, and the interposition of oneor more additional elements is contemplated, although not required.Conversely, the terms “directly coupled,” “directly connected,” etc.,imply the absence of such additional elements.

Transistors are typically shown as single devices for illustrativepurposes. However, it is understood by those with skill in the art thattransistors will have various sizes (e.g., gate width and length) andcharacteristics (e.g., threshold voltage, gain, etc.) and may consist ofmultiple transistors coupled in parallel to get desired electricalcharacteristics from the combination. Further, the illustratedtransistors may be composite transistors.

As used in the claims, the terms “source,” “drain,” and “gate” should beunderstood to refer either to the source, drain, and gate of a MOSFET orto the emitter, collector, and base of a bi-polar device when thepresent invention is implemented using bi-polar transistor technology.

1. A device, comprising: a current multiplier that multiplies a firstcurrent and a current proportional to absolute temperature to generate asecond current; an exponential converter that applies an exponentialtransfer function to the second current to generate an output current,the exponential transfer function depending on a thermal voltage, andtemperature dependence of the current proportional to absolutetemperature counteracting temperature dependence of the thermal voltageto cause the output current to be proportional to atemperature-independent, exponential function of the first current overan operating range of the device; and a current limiter that imposes atleast one of an upper limit and a lower limit on the output current, thecurrent limiter including a first reference-current source directlycoupled to an output terminal, an operational amplifier, a secondreference-current source coupled to a first input of the operationalamplifier, an output and a second input of the operational amplifierbeing connected via a feedback loop, the output current being applied tothe second input of the operational amplifier, and first and secondcurrent mirrors coupled between the second input of the operationalamplifier and the output terminal, the output terminal outputting alimited current, a reference current generated by the first referencecurrent source setting the lower limit, and a reference currentgenerated by the second reference current source setting the upperlimit.
 2. The device of claim 1, wherein, on a scale of the outputcurrent, the operating range is at least about 40 dB.
 3. The device ofclaim 1, further including a voltage scaler that generates the firstcurrent based on an input voltage and applies the first current, througha resistive load, to the current multiplier, and over the operatingrange the output current is proportional to a temperature-independent,exponential function of the input voltage.
 4. The device of claim 3,wherein the voltage scaler includes: a second operational amplifier; areference current source coupled to a first input of the secondoperational amplifier; and a feedback loop that connects an output and asecond input of the second operational amplifier, the input voltagebeing coupled to the first input of the second operational amplifierthrough a programmably variable resistor, and the output of the secondoperational amplifier being coupled to the resistive load.
 5. The deviceof claim 4, wherein: the reference current source is a programmablyvariable current source; and settings of the programmably variableresistor and of the programmably variable current source definerelationship between the input voltage and the first current.
 6. Thedevice of claim 1, wherein the current multiplier includes: first andsecond differential amplifiers, each having a corresponding currentmirror as a load; a first current source coupled as a tail supply of thefirst differential amplifier; and a second current source coupled as atail supply of the second differential amplifier, the second currentsource generating the current proportional to absolute temperature, thefirst differential amplifier receiving the first current, and the seconddifferential amplifier outputting the second current.
 7. The device ofclaim 6, wherein the first current source generates a reference currentthat is independent of technological process used for fabrication of thecurrent multiplier and of temperature.
 8. The device of claim 6,wherein: each of the first and second differential amplifiers comprisesa corresponding first transistor and a corresponding second transistor;gates of the first transistors are electrically connected to a firstcommon node; and gates of the second transistors are electricallyconnected to a second common node.
 9. The device of claim 1, wherein theexponential converter includes: a differential transistor paircomprising a first transistor and a second transistor; a resistor thatelectrically connects a gate of the first transistor and a gate of thesecond transistor; and a current source that drives a reference currentthrough the second transistor, the second current flowing through theresistor, and the output current flowing through the first transistor.10. The device of claim 9, wherein each of the first and secondtransistors is a MOSFET transistor that operates in a sub-threshold modeto enable the exponential converter to apply said exponential transferfunction.
 11. The device of claim 1, wherein the current multiplierincludes: first and second differential amplifiers, each having acorresponding current mirror as a load; a first current source coupledas a tail supply of the first differential amplifier; and a secondcurrent source coupled as a tail supply of the second differentialamplifier, each of the first and second differential amplifiersincluding a corresponding first transistor and a corresponding secondtransistor, gates of the first transistors being electrically connectedto receive a first common voltage, gates of the second transistors beingelectrically connected to receive a second common voltage, the firstcurrent source generating a reference current that is independent oftechnological process used for fabrication of the current multiplier andof temperature, the second current source generating the currentproportional to absolute temperature, the first differential amplifierreceiving the first current, and the second differential amplifieroutputting the second current; and the exponential converter includes: adifferential transistor pair including a third transistor and a fourthtransistor; a resistor that electrically connects a gate of the thirdtransistor and a gate of the fourth transistor; and a third currentsource that drives a corresponding reference current through the fourthtransistor, the second current flowing through the resistor, the outputcurrent flowing through the third transistor, and each of the third andfourth transistors being a MOSFET transistor operating in asub-threshold mode to enable the exponential converter to apply saidexponential transfer function.